Hundredths — Part 1
Semester 4B · Chapter 12 · Lesson 3 · MATH-4B-C12-L03
Before you begin: prerequisite check
Recall: 12.01; equivalence. Attempt these questions independently first.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 2nd tick after 2?
Show answer and reasoning
Each interval is 0.1, so add 2 tenths to 2 to get 2.2.
On a number line from 0 to 1 divided into ten equal intervals, what decimal is at the 4th tick after 0?
Show answer and reasoning
Each interval is 0.1, so add 4 tenths to 0 to get 0.4.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 7th tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 7 tenths to 4 to get 4.7.
Key vocabulary
- tenth
- one of ten equal parts of a whole
- hundredth
- one of one hundred equal parts
- equivalent decimals
- two notations for the same amount
- midpoint
- exact halfway point between rounding benchmarks
Understand the concept
Divide a whole into one hundred equal squares, arranged in a 10-by-10 grid. Thirty-six shaded squares represent 36/100, written 0.36. The second digit after the decimal point counts hundredths. One tenth contains ten hundredths, so three tenths contains thirty hundredths. Label the fixed whole on every grid. Shading only a single square means one hundredth, not one tenth. The decimal 0.07 means seven hundredths, not seven tenths.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Write 85/100 as a two-decimal-place number.
85 hundredths are 0.85.
Check 1: try it yourself
Write 57/100 as a two-decimal-place number.
Show answer and reasoning
57 hundredths are 0.57.
Worked example 2
Write 19/100 as a two-decimal-place number.
19 hundredths are 0.19.
Check 2: try it yourself
Write 79/100 as a two-decimal-place number.
Show answer and reasoning
79 hundredths are 0.79.
Worked example 3
Write 48/100 as a two-decimal-place number.
48 hundredths are 0.48.
Check 3: try it yourself
Write 91/100 as a two-decimal-place number.
Show answer and reasoning
91 hundredths are 0.91.
Guided practice
Write 56/100 as a two-decimal-place number.
Show answer and reasoning
56 hundredths are 0.56.
Write 83/100 as a two-decimal-place number.
Show answer and reasoning
83 hundredths are 0.83.
Write 17/100 as a two-decimal-place number.
Show answer and reasoning
17 hundredths are 0.17.
Write 12/100 as a two-decimal-place number.
Show answer and reasoning
12 hundredths are 0.12.
Write 82/100 as a two-decimal-place number.
Show answer and reasoning
82 hundredths are 0.82.
Independent practice
Write 98/100 as a two-decimal-place number.
Show answer and reasoning
98 hundredths are 0.98.
Write 53/100 as a two-decimal-place number.
Show answer and reasoning
53 hundredths are 0.53.
Write 77/100 as a two-decimal-place number.
Show answer and reasoning
77 hundredths are 0.77.
Write 59/100 as a two-decimal-place number.
Show answer and reasoning
59 hundredths are 0.59.
Write 90/100 as a two-decimal-place number.
Show answer and reasoning
90 hundredths are 0.90.
Write 35/100 as a two-decimal-place number.
Show answer and reasoning
35 hundredths are 0.35.
Write 68/100 as a two-decimal-place number.
Show answer and reasoning
68 hundredths are 0.68.
Write 95/100 as a two-decimal-place number.
Show answer and reasoning
95 hundredths are 0.95.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Write 65/100 as a two-decimal-place number. Explain how place value or a model can check your result.
Show answer and reasoning
65 hundredths are 0.65. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.04 means four tenths.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 0.04 means four hundredths; four tenths is 0.40. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Write 61/100 as a two-decimal-place number.
Show answer and reasoning
61 hundredths are 0.61.
Write 96/100 as a two-decimal-place number.
Show answer and reasoning
96 hundredths are 0.96.
Write 74/100 as a two-decimal-place number.
Show answer and reasoning
74 hundredths are 0.74.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.